Question

Homotopy groups of weighted projective space via homotopy sequence for Serre-fibrations

score 53 · Answer 1 · 2020-03-06 10:47:13

53

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Homotopy groups of weighted projective space via homotopy sequence for Serre-fibrations

Published on 06 Mar 2020 - 10:47

score 167 · Answer 2 · 2020-03-21 23:23:05

167

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Show that the space $Y = S^3 \vee S^6$ has precisely two distinct homotopy classes of comultiplications.

Published on 21 Mar 2020 - 23:23

score 148 · Answer 3 · 2020-04-10 14:00:41

148

Views

Infinitely generated $\pi_2(M)$ where $M$ is closed smooth manifold

Published on 10 Apr 2020 - 14:00

score 541 · Answer 4 · 2026-03-16 20:42:24

541

Views

The $n$-dimensional cube modulus its boundary is homeomorphic to an $n$-dimensional sphere

Published on 16 Mar 2026 - 20:42

score 129 · Answer 5 · 2020-04-30 12:59:01

129

Views

Why doesn't the Homotopy group satisfy excision?

Published on 30 Apr 2020 - 12:59

score 242 · Answer 6 · 2020-05-06 16:48:53

242

Views

Show that $S^2$ and $S^3 \times \mathbb CP^\infty$ have isomorphic homotopy groups.

Published on 06 May 2020 - 16:48

score 159 · Answer 7 · 2020-05-16 20:30:40

159

Views

Long exact sequence of the Klein bottle as a $S^1$-fiber bundle

Published on 16 May 2020 - 20:30

score 584 · Answer 8 · 2020-05-17 17:33:48

584

Views

Homotopy groups of $S^\infty$

Published on 17 May 2020 - 17:33

score 56 · Answer 9 · 2020-05-26 11:08:38

56

Views

Is composing homotopies of spheres bilinear?

Published on 26 May 2020 - 11:08

score 48 · Answer 10 · 2020-05-28 01:53:23

48

Views

$f:X\to Y$ extends to a map $Z\to Y$ iff $f_*[g] = 0$

Published on 28 May 2020 - 1:53

score 153 · Answer 11 · 2020-06-01 11:00:27

153

Views

Relative homotopy groups $\pi_k (S^n, S^1)$

Published on 01 Jun 2020 - 11:00

score 41 · Answer 12 · 2020-06-03 00:11:06

41

Views

Question regarding surjectivity of induced homormophism in an old version of Hatcher's proof of Prop. 4.13

Published on 03 Jun 2020 - 0:11

score 36 · Answer 13 · 2020-06-03 18:42:29

36

Views

CW approximation: why does $S^{n+1}\to X$ qualify as an attaching map for attaching $S^{n+1}$ to another space $Z$?

Published on 03 Jun 2020 - 18:42

score 78 · Answer 14 · 2026-02-23 08:42:02

78

Views

Does a deformation retraction of $X$ onto a subspace $A\subset X$ induce an isomorphism $\pi_n(X) \to \pi_n(A)$?

Published on 23 Feb 2026 - 8:42

score 839 · Answer 15 · 2020-06-16 13:30:34

839

Views

Homotopy groups of quotient groups.

Published on 16 Jun 2020 - 13:30

List Question

Homotopy groups of weighted projective space via homotopy sequence for Serre-fibrations

Show that the space $Y = S^3 \vee S^6$ has precisely two distinct homotopy classes of comultiplications.

Infinitely generated $\pi_2(M)$ where $M$ is closed smooth manifold

The $n$-dimensional cube modulus its boundary is homeomorphic to an $n$-dimensional sphere

Why doesn't the Homotopy group satisfy excision?

Show that $S^2$ and $S^3 \times \mathbb CP^\infty$ have isomorphic homotopy groups.

Long exact sequence of the Klein bottle as a $S^1$-fiber bundle

Homotopy groups of $S^\infty$

Is composing homotopies of spheres bilinear?

$f:X\to Y$ extends to a map $Z\to Y$ iff $f_*[g] = 0$

Relative homotopy groups $\pi_k (S^n, S^1)$

Question regarding surjectivity of induced homormophism in an old version of Hatcher's proof of Prop. 4.13

CW approximation: why does $S^{n+1}\to X$ qualify as an attaching map for attaching $S^{n+1}$ to another space $Z$?

Does a deformation retraction of $X$ onto a subspace $A\subset X$ induce an isomorphism $\pi_n(X) \to \pi_n(A)$?

Homotopy groups of quotient groups.

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